Finite Group Databasebeta

← #7687247

Subgroups — #7687247

Order 512.

4674 conjugacy classes of subgroups.

The subgroup lattice has 1250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59895C213yesmaximal, complemented
2#59497C213yesmaximal, complemented
3#59297C213yesmaximal, complemented
4#59292C213yesmaximal, complemented
5#59256C213yesmaximal, complemented
6#45383C213yesmaximal, complemented
7#45153C213yesmaximal, complemented
8#45012C213yesmaximal, complemented
9#44910C213yesmaximal, complemented
10#38278C213yesmaximal, complemented
11#38230C213yesmaximal, complemented
12#38072C213yesmaximal, complemented
13#37889C213yesmaximal, complemented
14#36475C211yesmaximal, characteristic, complemented
15#36448C211yesmaximal, characteristic, complemented
16#36432C211yesmaximal, characteristic
17#36432C211yesmaximal, characteristic
18#36431C211yesmaximal, characteristic, complemented
19#36380C213yesmaximal, complemented
20#36199C213yesmaximal, complemented
21#35971C211yesmaximal, characteristic, complemented
22#35883C211yesmaximal, characteristic, complemented
23#35868C211yesmaximal, characteristic, complemented
24#35786C211yesmaximal, characteristic, complemented
25#34808C213yesmaximal, complemented
26#34337C211yesmaximal, characteristic, complemented
27#34293C211yesmaximal, characteristic
28#34262C211yesmaximal, characteristic, complemented
29#34197C211yesmaximal, characteristic, complemented
30#34129C211yesmaximal, characteristic, complemented
31C4⋊C4×#41C211yesmaximal, characteristic, complemented
32C2×#557C2211yescharacteristic
33C2×#548C2211yescharacteristic
34C2×#519C2211yescharacteristic
35C2×C4×#41C2211yescharacteristic
36C2×C4×#41C2211yescharacteristic
37C2×C4×#41C2211yescharacteristic
38#2864C2213yes—
39#2863C2213yes—
40#2855C2213yes—
41#2855C2213yes—
42#2851C2213yes—
43#2787C2216yes—
44#2787C2216yes—
45#2779C2216yes—
46#2779C2216yes—
47#2771C2216yes—
48#2770C2216yes—
49#2770C2216yes—
50#2765C2216yes—
51#2764C2216yes—
52#2761C2216yes—
53#2744C2216yes—
54#2739C2216yes—
55#2738C2216yes—
56#2694C2216yes—
57#2647C2213yes—
58#2647C2213yes—
59#2645C2213yes—
60#2629C2213yes—
61#2611C2216yes—
62#2601C2216yes—
63#2599C2216yes—
64#2582C2213yes—
65#2580C2213yes—
66#2573C2216yes—
67#2571C2213yes—
68#2570C2213yes—
69#2570C2213yes—
70#2570C2213yes—
71#2570C2213yes—
72#2566C2213yes—
73#2565C2213yes—
74#2552C2213yes—
75#2533C2213yes—
76#2532C2213yes—
77#2529C2213yes—
78#2529C2216yes—
79#2528C2216yes—
80#2528C2216yes—
81#2528C2213yes—
82#2527C2216yes—
83#2525C2211yescharacteristic
84#2524C2213yes—
85#2524C2216yes—
86#2520C2213yes—
87#2519C2213yes—
88#2515C2216yes—
89#2514C2213yes—
90#2514C2213yes—
91#2514C2213yes—
92#2514C2213yes—
93#2511C2213yes—
94#2511C2213yes—
95#2509C2213yes—
96#2509C2213yes—
97#2509C2213yes—
98#2508C2213yes—
99#2508C2213yes—
100#2508C2216yes—
101#2508C2213yes—
102#2507C2213yes—
103#2507C2213yes—
104#2507C2213yes—
105#2506C2213yes—
106#2506C2213yes—
107#2506C2213yes—
108#2499C2213yes—
109#2499C2213yes—
110#2498C2213yes—
111#2497C2213yes—
112#2496C2213yes—
113#2495C2213yes—
114#2495C2213yes—
115#2494C2213yes—
116#2494C2213yes—
117#2494C2216yes—
118#2493C2216yes—
119#2493C2213yes—
120#2488C2213yes—
121#2485C2213yes—
122#2485C2213yes—
123#2484C2216yes—
124#2484C2213yes—
125#2481C2213yes—
126#2475C2216yes—
127#2473C2213yes—
128#2473C2216yes—
129#2458C2216yes—
130#2454C2213yes—
131#2453C2213yes—
132#2452C2213yes—
133#2451C2213yes—
134#2447C2213yes—
135#2447C2213yes—
136#2447C2213yes—
137#2447C2213yes—
138#2441C2213yes—
139#2441C2213yes—
140#2439C2213yes—
141#2439C2213yes—
142#2438C2213yes—
143#2422C2213yes—
144#2422C2213yes—
145#2421C2216yes—
146#2420C2213yes—
147#2420C2213yes—
148#2413C2213yes—
149#2402C2213yes—
150#2402C2213yes—
151#2401C2213yes—
152#2396C2213yes—
153#2371C2216yes—
154#2370C2213yes—
155#2370C2213yes—
156#2367C2213yes—
157#2365C2213yes—
158#2363C2213yes—
159#2362C2213yes—
160#2357C2213yes—
161#2357C2213yes—
162#2356C2216yes—
163#2356C2213yes—
164#2355C2213yes—
165#2354C2213yes—
166#2354C2213yes—
167#2354C2213yes—
168#2351C2211yescharacteristic
169#2351C2211yescharacteristic
170#2351C2211yescharacteristic
171#2351C2211yescharacteristic
172#2351C2211yescharacteristic
173#2351C2211yescharacteristic
174#2351C2211yescharacteristic
175#2351C2211yescharacteristic
176Q8×C4⋊C4C2211yescharacteristic
177Q8×C4⋊C4C2211yescharacteristic
178Q8×C4⋊C4C2211yescharacteristic
179Q8×C4⋊C4C2211yescharacteristic
180Q8×C4⋊C4C2211yescharacteristic
181Q8×C4⋊C4C2211yescharacteristic
182Q8×C4⋊C4C2213yes—
183Q8×C4⋊C4C2211yescharacteristic
184Q8×C4⋊C4C2211yescharacteristic
185#2349C2213yes—
186#2349C2213yes—
187D4×C4⋊C4C2213yes—
188D4×C4⋊C4C2213yes—
189#2347C2213yes—
190#2346C2213yes—
191#2346C2213yes—
192#2346C2213yes—
193#2346C2213yes—
194#2346C2213yes—
195#2343C2216yes—
196#2341C2211yescharacteristic
197#2341C2211yescharacteristic
198#2341C2211yescharacteristic
199Q8×C22⋊C4C2211yescharacteristic
200Q8×C22⋊C4C2211yescharacteristic
201Q8×C22⋊C4C2211yescharacteristic
202Q8×C22⋊C4C2211yescharacteristic
203Q8×C22⋊C4C2211yescharacteristic
204#2330C2213yes—
205#2330C2213yes—
206#2326C2213yes—
207#2324C2213yes—
208#2320C2213yes—
209#2319C2213yes—
210#2319C2213yes—
211#2314C2213yes—
212C4×C4⋊Q8C2213yes—
213C4×#125C2213yes—
214C4×#126C2213yes—
215C4×C22⋊Q8C2213yes—
216C4×C22⋊Q8C2213yes—
217C4×#123C2213yes—
218C4×#123C2213yes—
219#2298C2213yes—
220#2296C2213yes—
221#2296C2213yes—
222#2295C2213yes—
223#2295C2213yes—
224#2293C2213yes—
225#2293C2213yes—
226#2290C2213yes—
227#2285C2213yes—
228#2285C2213yes—
229#2283C2213yes—
230#2283C2213yes—
231#2276C2211yescharacteristic
232#2276C2211yescharacteristic
233#2276C2211yescharacteristic
234C42×Q8C2211yescharacteristic
235C42×Q8C2211yescharacteristic
236C4×#117C2213yes—
237C2×C4×C4⋊C4C2213yes—
238C22×#41C2311yescharacteristic
239C23×Q8C2311yescharacteristic
240#557—28no—
241#548—28no—
242C2×C4⋊Q8C2313yes—
243C2×#126C2313yes—
244C2×#125C2313yes—
245C2×#125C2313yes—
246C2×#125C2313yes—
247C2×#125C2316yes—
248C2×#124C2313yes—
249C2×#123C2313yes—
250C2×#123C2313yes—
251C2×C22⋊Q8C2313yes—
252C2×C22⋊Q8C2313yes—
253C2×#121C2313yes—
254#519—28no—
255C4×#41—28no—
256C4×#41—28no—
257C4×#41—28no—
258C2×C4×Q8C2313yes—
259C2×C4×Q8C2313yes—
260C2×C4×Q8C2313yes—
261C2×C4×Q8C2311yescharacteristic
262C2×C4×Q8C2311yescharacteristic
263C2×C4×Q8C2311yescharacteristic
264C2×C4×Q8C2311yescharacteristic
265C2×C4×Q8C2311yescharacteristic
266C2×C4×Q8C2311yescharacteristic
267C2×C4×Q8C2311yescharacteristic
268C2×C4×Q8C2311yescharacteristic
269C2×C4×Q8C2311yescharacteristic
270C2×C4×Q8C2311yescharacteristic
271C2×C4×Q8C2311yescharacteristic
272C2×C4×Q8C2311yescharacteristic
273C2×C4×Q8C2316yes—
274C2×C4×Q8C2311yescharacteristic
275C2×C4×D4C2313yes—
276C2×C4×D4C2313yes—
277C2×C4×D4C2313yes—
278C2×C4×D4C2313yes—
279C2×C4×D4C2313yes—
280C2×C4×D4C2313yes—
281C2×C4×D4C2313yes—
282C2×#117C2313yes—
283C2×#117C2313yes—
284C2×#117C2313yes—
285C2×#117C2313yes—
286C2×#117C2313yes—
287C2×#117C2316yes—
288C2×#117C2313yes—
289C2×#117C2313yes—
290C22×C4⋊C4C2313yes—
291C22×C4⋊C4C2313yes—
292C22×C42C2313yes—
293C22×C42C2313yes—
294C22×C42C2313yes—
295#401C2316yes—
296#401C2313yes—
297#401C2316yes—
298#400C2313yes—
299#400C2316yes—
300#400C2316yes—
301#400C2316yes—
302#400C2313yes—
303#400C2313yes—
304#400C2316yes—
305#400C2316yes—
306#400C2313yes—
307#400C2316yes—
308#400C2313yes—
309#400C2316yes—
310#400C2316yes—
311#400C2313yes—
312#400C2313yes—
313#400C2313yes—
314#400C2311yescharacteristic
315#400C2313yes—
316#400C2313yes—
317#400C2313yes—
318#400C2316yes—
319#399C2316yes—
320#399C2313yes—
321#398C2313yes—
322#398C2316yes—
323#398C2313yes—
324#398C2316yes—
325#398C2316yes—
326#398C2316yes—
327#398C2313yes—
328#398C2313yes—
329#398C2316yes—
330#398C2316yes—
331#398C2313yes—
332#398C2316yes—
333#398C2311yescharacteristic
334#398C2313yes—
335#398C2313yes—
336#398C2313yes—
337#398C2313yes—
338#397C2316yes—
339#397C2316yes—
340#397C2316yes—
341#397C2311yescharacteristic
342#397C2313yes—
343#397C2313yes—
344#397C2316yes—
345#397C2316yes—
346#397C2316yes—
347#397C2316yes—
348#396C2316yes—
349#396C2316yes—
350#396C2316yes—
351#396C2313yes—
352#396C2311yescharacteristic
353#396C2313yes—
354#395C2313yes—
355#394C2316yes—
356#394C2316yes—
357#393C2316yes—
358#393C2313yes—
359#391C2313yes—
360#391C2313yes—
361#391C2313yes—
362#391C2313yes—
363#391C2313yes—
364#391C2313yes—
365#391C2313yes—
366#391C2313yes—
367#391C2316yes—
368#391C2313yes—
369#391C2313yes—
370#391C2313yes—
371#391C2313yes—
372#391C2313yes—
373#390C2313yes—
374#390C2313yes—
375#390C2313yes—
376#390C2313yes—
377#390C2313yes—
378#390C2316yes—
379#390C2313yes—
380#389C2313yes—
381#389C2313yes—
382#389C2316yes—
383#389C2313yes—
384#389C2313yes—
385#389C2313yes—
386#389C2313yes—
387#389C2313yes—
388#389C2313yes—
389#389C2313yes—
390#389C2313yes—
391#389C2313yes—
392#389C2313yes—
393#389C2316yes—
394#389C2313yes—
395#389C2316yes—
396#389C2313yes—
397#389C2313yes—
398#389C2313yes—
399#389C2313yes—
400#389C2313yes—
401#389C2313yes—
402#389C2313yes—
403#389C2316yes—
404#389C2313yes—
405#389C2316yes—
406#389C2313yes—
407#389C2316yes—
408#389C2313yes—
409#389C2313yes—
410#389C2313yes—
411#389C2313yes—
412#389C2313yes—
413#389C2313yes—
414#389C2313yes—
415#389C2313yes—
416#389C2313yes—
417#389C2313yes—
418#389C2313yes—
419#389C2313yes—
420#389C2313yes—
421#389C2313yes—
422#389C2311yescharacteristic
423#388C2311yescharacteristic
424#388C2313yes—
425#388C2313yes—
426#388C2313yes—
427#388C2316yes—
428#388C2316yes—
429#388C2316yes—
430#388C2316yes—
431#388C2316yes—
432#388C2316yes—
433#388C2316yes—
434#388C2316yes—
435#388C2316yes—
436#388C2313yes—
437#388C2316yes—
438#388C2316yes—
439#388C2316yes—
440#388C2316yes—
441#388C2313yes—
442#388C2313yes—
443#388C2311yescharacteristic
444#388C2313yes—
445#388C2313yes—
446#388C2311yescharacteristic
447#388C2311yescharacteristic
448#388C2311yescharacteristic
449#387C2313yes—
450#387C2313yes—
451#387C2313yes—
452#387C2311yescharacteristic
453#387C2313yes—
454#387C2313yes—
455#387C2313yes—
456#387C2316yes—
457#387C2316yes—
458#387C2316yes—
459#387C2316yes—
460#387C2316yes—
461#387C2316yes—
462#387C2316yes—
463#387C2316yes—
464#387C2316yes—
465#387C2316yes—
466#387C2313yes—
467#387C2313yes—
468#387C2313yes—
469#387C2316yes—
470#387C2313yes—
471#387C2316yes—
472#387C2316yes—
473#387C2316yes—
474#387C2316yes—
475#387C2313yes—
476#387C2313yes—
477#387C2316yes—
478#387C2316yes—
479#387C2316yes—
480#387C2316yes—
481#387C2316yes—
482#387C2313yes—
483#387C2313yes—
484#387C2313yes—
485#387C2313yes—
486#387C2313yes—
487#387C2313yes—
488#387C2313yes—
489#387C2313yes—
490#387C2313yes—
491#387C2311yescharacteristic
492#386C2313yes—
493#386C2313yes—
494#386C2313yes—
495#386C2313yes—
496#385C2313yes—
497#385C2316yes—
498#385C2316yes—
499#385C2316yes—
500#385C2313yes—
501#385C2313yes—
502#385C2316yes—
503#385C2316yes—
504#385C2316yes—
505#385C2316yes—
506#385C2316yes—
507#385C2316yes—
508#385C2313yes—
509#385C2313yes—
510#385C2313yes—
511#384C2313yes—
512#384C2313yes—
513#384C2313yes—
514#384C2313yes—
515#384C2313yes—
516#384C2313yes—
517#384C2313yes—
518#384C2313yes—
519#383C2313yes—
520#383C2316yes—
521#383C2316yes—
522#383C2316yes—
523#383C2313yes—
524#383C2311yescharacteristic
525#382C2313yes—
526#382C2313yes—
527#382C2313yes—
528#382C2313yes—
529#382C2313yes—
530#382C2313yes—
531#382C2313yes—
532#382C2313yes—
533#382C2313yes—
534#382C2316yes—
535#382C2316yes—
536#382C2313yes—
537#382C2316yes—
538#382C2313yes—
539#381C2313yes—
540#381C2316yes—
541#381C2316yes—
542#381C2316yes—
543#381C2313yes—
544#381C2313yes—
545#381C2313yes—
546#380C2313yes—
547#380C2313yes—
548#380C2313yes—
549#380C2313yes—
550#380C2313yes—
551#380C2313yes—
552#380C2313yes—
553#380C2313yes—
554#380C2313yes—
555#380C2313yes—
556#380C2316yes—
557#380C2316yes—
558#380C2316yes—
559#380C2313yes—
560C4×C4⋊C4C2313yes—
561C4×C4⋊C4C2313yes—
562C4×C4⋊C4C2313yes—
563C4×C4⋊C4C2313yes—
564C4×C4⋊C4C2313yes—
565C4×C4⋊C4C2313yes—
566C4×C4⋊C4C2313yes—
567C4×C4⋊C4C2313yes—
568C4×C4⋊C4C2313yes—
569C4×C4⋊C4C2313yes—
570C4×C4⋊C4C2316yes—
571C4×C4⋊C4C2313yes—
572C4×C4⋊C4C2313yes—
573C4×C4⋊C4C2313yes—
574C4×C4⋊C4C2313yes—
575C4×C4⋊C4C2313yes—
576C4×C4⋊C4C2313yes—
577C4×C4⋊C4C2313yes—
578C4×C4⋊C4C2316yes—
579C4×C4⋊C4C2313yes—
580C4×C4⋊C4C2313yes—
581C4×C4⋊C4C2313yes—
582C4×C4⋊C4C2313yes—
583C4×C4⋊C4C2313yes—
584C4×C4⋊C4C2313yes—
585C4×C4⋊C4C2313yes—
586C4×C4⋊C4C2313yes—
587C4×C4⋊C4C2313yes—
588C4×C4⋊C4C2313yes—
589C4×C4⋊C4C2313yes—
590C4×C4⋊C4C2313yes—
591C4×C4⋊C4C2316yes—
592C4×C4⋊C4C2313yes—
593C4×C4⋊C4C2316yes—
594C4×C4⋊C4C2313yes—
595C4×C4⋊C4C2313yes—
596C4×C4⋊C4C2313yes—
597C4×C4⋊C4C2311yescharacteristic
598C4×C4⋊C4C2311yescharacteristic
599C4×C4⋊C4C2313yes—
600C4×C4⋊C4C2313yes—
601C4×C22⋊C4C2313yes—
602C4×C22⋊C4C2313yes—
603C4×C22⋊C4C2313yes—
604C4×C22⋊C4C2316yes—
605C4×C22⋊C4C2313yes—
606C4×C22⋊C4C2313yes—
607C4×C22⋊C4C2313yes—
608C4×C22⋊C4C2313yes—
609C4×C22⋊C4C2313yes—
610C4×C22⋊C4C2316yes—
611C4×C22⋊C4C2313yes—
612C4×C22⋊C4C2313yes—
613#376C2313yes—
614#376C2313yes—
615#376C2313yes—
616#376C2316yes—
617#376C2313yes—
618#376C2316yes—
619#376C2313yes—
620C2×#95C2313yes—
621C2×#95C2313yes—
622C43C2313yes—
623C43C2313yes—
624C2×#41—24no—
625C2×#41—24no—
626C2×#41#4118yes—
627C22×Q8—24no—
628C22×Q8—24no—
629C22×Q8—24no—
630C22×Q8C2413yes—
631C22×Q8C2413yes—
632C22×Q8C2411yescharacteristic
633C22×D4C2413yes—
634C22×D4C2413yes—
635C23×C4C2413yes—
636C23×C4C2413yes—
637C23×C4C2413yes—
638C23×C4C2413yes—
639C23×C4C2413yes—
640C23×C4C2413yes—
641C23×C4C2413yes—
642C23×C4C2413yes—
643C4⋊Q8—212no—
644#126—46no—
645#125—212no—
646#125—212no—
647#125—46no—
648#125—412no—
649#124—212no—
650#123—46no—
651#123—46no—
652C22⋊Q8—212no—
653C22⋊Q8—46no—
654#121—212no—
655C4×Q8—24no—
656C4×Q8—24no—
657C4×Q8—24no—
658C4×Q8—24no—
659C4×Q8—24no—
660C4×Q8—24no—
661C4×Q8—24no—
662C4×Q8—24no—
663C4×Q8—24no—
664C4×Q8—24no—
665C4×Q8—24no—
666C4×Q8—24no—
667C4×Q8—212no—
668C4×Q8—212no—
669C4×Q8—212no—
670C4×Q8—412no—
671C4×Q8#4118yes—
672C4×D4—212no—
673C4×D4—212no—
674C4×D4—212no—
675C4×D4—212no—
676C4×D4—212no—
677C4×D4—212no—
678C4×D4—212no—
679#117—212no—
680#117—212no—
681#117—212no—
682#117—212no—
683#117—212no—
684#117—412no—
685#117—46no—
686#117—46no—
687C2×C4⋊C4—46no—
688C2×C4⋊C4—46no—
689C2×C4⋊C4C2411yescharacteristic
690C2×C4⋊C4C2411yescharacteristic
691C2×C4⋊C4C2413yes—
692C2×C4⋊C4C2413yes—
693C2×C4⋊C4C2411yescharacteristic
694C2×C4⋊C4C2411yescharacteristic
695C2×C4⋊C4C2413yes—
696C2×C4⋊C4C2413yes—
697C2×C4⋊C4C2413yes—
698C2×C4⋊C4C2413yes—
699C2×C4⋊C4C2413yes—
700C2×C4⋊C4C2413yes—
701C2×C4⋊C4C2413yes—
702C2×C4⋊C4C2413yes—
703C2×C4⋊C4C2413yes—
704C2×C4⋊C4C2413yes—
705C2×C4⋊C4C2411yescharacteristic
706C2×C4⋊C4C2413yes—
707C2×C4⋊C4C2413yes—
708C2×C4⋊C4C2413yes—
709C2×C4⋊C4C2413yes—
710C2×C4⋊C4C2413yes—
711C2×C4⋊C4C2413yes—
712C2×C4⋊C4C2413yes—
713C2×C4⋊C4C2413yes—
714C2×C4⋊C4C2413yes—
715C2×C4⋊C4C2411yescharacteristic
716C2×C4⋊C4C2413yes—
717C2×C4⋊C4C2411yescharacteristic
718C2×C4⋊C4C2416yes—
719C2×C4⋊C4C2413yes—
720C2×C4⋊C4C2413yes—
721C2×C4⋊C4C2413yes—
722C2×C4⋊C4C2413yes—
723C2×C4⋊C4C2413yes—
724C2×C4⋊C4C2416yes—
725C2×C4⋊C4C2416yes—
726C2×C4⋊C4C2416yes—
727C2×C4⋊C4C2416yes—
728C2×C4⋊C4C2413yes—
729C2×C4⋊C4C2413yes—
730C2×C4⋊C4C2413yes—
731C2×C4⋊C4C2413yes—
732C2×C4⋊C4C2413yes—
733C2×C4⋊C4C2413yes—
734C2×C4⋊C4C2416yes—
735C2×C4⋊C4C2416yes—
736C2×C4⋊C4C2413yes—
737C2×C4⋊C4C2413yes—
738C2×C4⋊C4C2416yes—
739C2×C4⋊C4C2413yes—
740C2×C4⋊C4C2413yes—
741C2×C4⋊C4C2413yes—
742C2×C4⋊C4C2411yescharacteristic
743C2×C4⋊C4C2411yescharacteristic
744C2×C4⋊C4C2416yes—
745C2×C4⋊C4C2413yes—
746C2×C4⋊C4C2413yes—
747C2×C4⋊C4C2413yes—
748C2×C4⋊C4C2413yes—
749C2×C22⋊C4C2411yescharacteristic
750C2×C22⋊C4C2413yes—
751C2×C22⋊C4C2416yes—
752C2×C22⋊C4C2416yes—
753C2×C22⋊C4C2416yes—
754C2×C22⋊C4C2413yes—
755C2×C22⋊C4C2411yescharacteristic
756C2×C22⋊C4C2413yes—
757C2×C22⋊C4C2416yes—
758C2×C22⋊C4C2411yescharacteristic
759C2×C22⋊C4C2411yescharacteristic
760C2×C22⋊C4C2411yescharacteristic
761C2×C22⋊C4C2416yes—
762C2×C22⋊C4C2413yes—
763C2×C22⋊C4C2413yes—
764C2×C22⋊C4C2413yes—
765C2×C22⋊C4C2416yes—
766C2×C22⋊C4C2413yes—
767C2×C22⋊C4C2413yes—
768C2×C22⋊C4C2413yes—
769C2×C22⋊C4C2413yes—
770C2×C22⋊C4C2413yes—
771C2×C22⋊C4C2413yes—
772C2×C22⋊C4C2411yescharacteristic
773C2×C22⋊C4C2411yescharacteristic
774C2×C22⋊C4C2413yes—
775C2×C22⋊C4C2416yes—
776C2×C42—212no—
777C2×C42—212no—
778C2×C42—212no—
779C2×C42C2413yes—
780C2×C42C2413yes—
781C2×C42C2413yes—
782C2×C42C2413yes—
783C2×C42C2413yes—
784C2×C42C2413yes—
785C2×C42C2413yes—
786C2×C42C2416yes—
787C2×C42C2413yes—
788C2×C42C2413yes—
789C2×C42C2413yes—
790C2×C42C2413yes—
791C2×C42C2413yes—
792C2×C42C2413yes—
793C2×C42C2413yes—
794C2×C42C2413yes—
795C2×C42C2413yes—
796C2×C42C2413yes—
797C2×C42C2413yes—
798C2×C42C2411yescharacteristic
799C2×C42C2411yescharacteristic
800C2×C42C2411yescharacteristic
801C2×C42C2413yes—
802C2×C42C2413yes—
803C2×C42C2413yes—
804C2×C42C2416yes—
805C2×C42C2416yes—
806C2×C42C2416yes—
807C2×C42C2411yescharacteristic
808C2×C42C2411yescharacteristic
809C2×C42C2413yes—
810#95C2411yescharacteristic
811#95C2411yescharacteristic
812#95C2413yes—
813#95C2413yes—
814#95C2413yes—
815#95C2413yes—
816#95C2413yes—
817#95C2413yes—
818#95C2411yescharacteristic
819#95C2411yescharacteristic
820#95C2413yes—
821#95C2411yescharacteristic
822#95C2411yescharacteristic
823#95C2411yescharacteristic
824#95C2413yes—
825#95C2413yes—
826#95C2413yes—
827#95C2413yes—
828#95C2413yes—
829#95C2413yes—
830#95C2413yes—
831#95C2413yes—
832#95C2413yes—
833#95C2413yes—
834#95C2413yes—
835#95C2413yes—
836#95C2413yes—
837#95C2413yes—
838#95C2413yes—
839#95C2413yes—
840#95C2416yes—
841#95C2416yes—
842#95C2416yes—
843#95C2416yes—
844#95C2411yescharacteristic
845#95C2413yes—
846#95C2413yes—
847#95C2413yes—
848#95C2413yes—
849#95C2413yes—
850#95C2413yes—
851#95C2413yes—
852#95C2413yes—
853#95C2413yes—
854#95C2413yes—
855#95C2413yes—
856#95C2413yes—
857#95C2411yescharacteristic
858#95C2416yes—
859#95C2416yes—
860#95C2411yescharacteristic
861#95C2411yescharacteristic
862#95C2411yescharacteristic
863#95C2411yescharacteristic
864#95C2413yes—
865#95C2411yescharacteristic
866#95C2416yes—
867#95C2416yes—
868#95C2416yes—
869#95C2416yes—
870#95C2413yes—
871#95C2413yes—
872#95C2413yes—
873#95C2413yes—
874#95C2413yes—
875#95C2413yes—
876#95C2413yes—
877#95C2413yes—
878#95C2413yes—
879#95C2413yes—
880#95C2416yes—
881#95C2416yes—
882#95C2416yes—
883#95C2416yes—
884#95C2416yes—
885C24C2511yescharacteristic
886C24C2513yes—
887#41—232no—
888C2×Q8—26no—
889C2×Q8—26no—
890C2×Q8—26no—
891C2×Q8—26no—
892C2×Q8—26no—
893C2×Q8—43no—
894C2×Q8—416no—
895C2×Q8C2×#4114yes—
896C2×Q8C2×#4114yes—
897C2×Q82−1+414yes—
898C2×D4—26no—
899C2×D4—26no—
900C2×D4—26no—
901C2×D4—43no—
902C2×D4—43no—
903C2×D4C2×#41112yes—
904C22×C4—26no—
905C22×C4—26no—
906C22×C4—26no—
907C22×C4—26no—
908C22×C4—26no—
909C22×C4—26no—
910C22×C4—26no—
911C22×C4—26no—
912C22×C4—26no—
913C22×C4—26no—
914C22×C4—26no—
915C22×C4—26no—
916C22×C4—26no—
917C22×C4—43no—
918C22×C4—43no—
919C22×C4—43no—
920C22×C4—43no—
921C22×C4—43no—
922C22×C4—43no—
923C22×C4—43no—
924C22×C4—43no—
925C22×C4—43no—
926C22×C4—43no—
927C22×C4C2×#41112yes—
928C22×C4C2513yes—
929C22×C4C2511yescharacteristic
930C22×C4C2511yescharacteristic
931C22×C4C2511yescharacteristic
932C22×C4C2511yescharacteristic
933C22×C4C2511yescharacteristic
934C22×C4C2513yes—
935C22×C4C2513yes—
936C22×C4C2511yescharacteristic
937C22×C4C2513yes—
938C22×C4C2513yes—
939C22×C4C2513yes—
940C22×C4C2513yes—
941C22×C4C2511yescharacteristic
942C22×C4C2513yes—
943C22×C4C2513yes—
944C22×C4C2511yescharacteristic
945C22×C4C2513yes—
946C22×C4C2513yes—
947C22×C4C2513yes—
948C22×C4C2511yescharacteristic
949C22×C4C2513yes—
950C22×C4C2511yescharacteristic
951C22×C4C2513yes—
952C22×C4C2511yescharacteristic
953C22×C4C2511yescharacteristic
954C22×C4C2511yescharacteristic
955C22×C4C2511yescharacteristic
956C22×C4C2513yes—
957C4⋊C4—26no—
958C4⋊C4—26no—
959C4⋊C4—26no—
960C4⋊C4—26no—
961C4⋊C4—26no—
962C4⋊C4—26no—
963C4⋊C4—26no—
964C4⋊C4—26no—
965C4⋊C4—26no—
966C4⋊C4—22no—
967C4⋊C4—26no—
968C4⋊C4—26no—
969C4⋊C4—26no—
970C4⋊C4—26no—
971C4⋊C4—26no—
972C4⋊C4—212no—
973C4⋊C4—26no—
974C4⋊C4—26no—
975C4⋊C4—26no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—26no—
979C4⋊C4—26no—
980C4⋊C4—22no—
981C4⋊C4—22no—
982C4⋊C4—26no—
983C4⋊C4—26no—
984C4⋊C4—22no—
985C4⋊C4—26no—
986C4⋊C4—22no—
987C4⋊C4—43no—
988C4⋊C4—43no—
989C4⋊C4—43no—
990C4⋊C4—43no—
991C4⋊C4—41no—
992C4⋊C4—43no—
993C4⋊C4—46no—
994C4⋊C4—43no—
995C4⋊C4—43no—
996C4⋊C4—41no—
997C4⋊C4—43no—
998C4⋊C4—43no—
999C4⋊C4—46no—
1000C4⋊C4—46no—
1001C4⋊C4—46no—
1002C4⋊C4—46no—
1003C4⋊C4—43no—
1004C4⋊C4—43no—
1005C4⋊C4—43no—
1006C4⋊C4—43no—
1007C4⋊C4—43no—
1008C4⋊C4—43no—
1009C4⋊C4—43no—
1010C4⋊C4—43no—
1011C4⋊C4—46no—
1012C4⋊C4—46no—
1013C4⋊C4—46no—
1014C4⋊C4—43no—
1015C4⋊C4—43no—
1016C4⋊C4C2×#41112yes—
1017C22⋊C4—212no—
1018C22⋊C4—212no—
1019C22⋊C4—26no—
1020C22⋊C4—212no—
1021C22⋊C4—26no—
1022C22⋊C4—22no—
1023C22⋊C4—212no—
1024C22⋊C4—22no—
1025C22⋊C4—26no—
1026C22⋊C4—22no—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—46no—
1032C22⋊C4—43no—
1033C22⋊C4—43no—
1034C22⋊C4—46no—
1035C22⋊C4—46no—
1036C22⋊C4—43no—
1037C22⋊C4—43no—
1038C22⋊C4—43no—
1039C22⋊C4—43no—
1040C22⋊C4—43no—
1041C22⋊C4—43no—
1042C22⋊C4—43no—
1043C22⋊C4—43no—
1044C42—22no—
1045C42—22no—
1046C42—22no—
1047C42—26no—
1048C42—26no—
1049C42—26no—
1050C42—26no—
1051C42—26no—
1052C42—26no—
1053C42—26no—
1054C42—26no—
1055C42—26no—
1056C42—212no—
1057C42—26no—
1058C42—26no—
1059C42—26no—
1060C42—26no—
1061C42—26no—
1062C42—26no—
1063C42—26no—
1064C42—26no—
1065C42—26no—
1066C42—41no—
1067C42—41no—
1068C42—43no—
1069C42—43no—
1070C42—43no—
1071C42—46no—
1072C42—46no—
1073C42—46no—
1074C42C2×#41112yes—
1075C23—23no—
1076C23—23no—
1077C23—23no—
1078C23—23no—
1079C23—23no—
1080C23—23no—
1081C23—21no—
1082C23—21no—
1083C23—21no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23C22×#4116yes—
1089C23C2611yescharacteristic
1090Q8—412no—
1091Q8—412no—
1092Q8#552116yes—
1093D4—224no—
1094D4—86no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—23no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—23no—
1107C2×C4—224no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—23no—
1114C2×C4—21no—
1115C2×C4—23no—
1116C2×C4—23no—
1117C2×C4—23no—
1118C2×C4—23no—
1119C2×C4—23no—
1120C2×C4—23no—
1121C2×C4—23no—
1122C2×C4—23no—
1123C2×C4—23no—
1124C2×C4—23no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—23no—
1129C2×C4—23no—
1130C2×C4—23no—
1131C2×C4—23no—
1132C2×C4—23no—
1133C2×C4—23no—
1134C2×C4—23no—
1135C2×C4—23no—
1136C2×C4—23no—
1137C2×C4—23no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—23no—
1142C2×C4—23no—
1143C2×C4—23no—
1144C2×C4—23no—
1145C2×C4—23no—
1146C2×C4—23no—
1147C2×C4—23no—
1148C2×C4—23no—
1149C2×C4—23no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—23no—
1155C2×C4—23no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—23no—
1159C2×C4—23no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—23no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—23no—
1168C2×C4—23no—
1169C2×C4—23no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—23no—
1174C2×C4—412no—
1175C2×C4—412no—
1176C2×C4—412no—
1177C2×C4—412no—
1178C2×C4—86no—
1179C2×C4—86no—
1180C2×C4—86no—
1181C2×C4C22×#4112yes—
1182C2×C4C22×#4116yes—
1183C2×C4C22×#4112yes—
1184C2×C4C22×#4116yes—
1185C2×C4C22×#4116yes—
1186C2×C4C2×2−1+416yes—
1187C2×C4#58512yes—
1188C2×C4#58512yes—
1189C2×C4#58512yes—
1190C22—26no—
1191C22—26no—
1192C22—26no—
1193C22—43no—
1194C22—43no—
1195C22—43no—
1196C22—43no—
1197C22—41no—
1198C22—41no—
1199C22—41no—
1200C22—41no—
1201C22—41no—
1202C22—41no—
1203C22—41no—
1204C22C23×#4111yescharacteristic
1205C22C23×#4111yescharacteristic
1206C22C22×2−1+411yescharacteristic
1207C22C2×#58511yescharacteristic
1208C22C2×#58511yescharacteristic
1209C22C2×#58511yescharacteristic
1210C222−1+611yescharacteristic
1211C4—22no—
1212C4—26no—
1213C4—22no—
1214C4—22no—
1215C4—22no—
1216C4—22no—
1217C4—41no—
1218C4—41no—
1219C4—43no—
1220C4—43no—
1221C4—41no—
1222C4—41no—
1223C4—43no—
1224C4—41no—
1225C4—43no—
1226C4—43no—
1227C4—43no—
1228C4—41no—
1229C4—43no—
1230C4—43no—
1231C4—43no—
1232C4—43no—
1233C4—41no—
1234C4—43no—
1235C4—41no—
1236C4—41no—
1237C4—43no—
1238C4—43no—
1239C4C2×#552112yes—
1240C2—46no—
1241C2—81no—
1242C2C22×#55211yescharacteristic
1243C2#6279311yescharacteristic
1244C2#6281611yescharacteristic
1245C2#6295311yescharacteristic
1246C2#6299311yescharacteristic
1247C2#6299311yescharacteristic
1248C2#6303411yescharacteristic
subgroupG/H
center, commutator, Frattini, socle, cosocleC23C26
prime radicalC2×#548C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23 ◁ G
LECSG ▷ C23 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #59895C2semidirect
2. #59497C2semidirect
3. #59297C2semidirect
4. #59292C2semidirect
5. #59256C2semidirect
6. #45383C2semidirect
7. #45153C2semidirect
8. #45012C2semidirect
9. #44910C2semidirect
10. #38278C2semidirect
11. #38230C2semidirect
12. #38072C2semidirect
13. #37889C2semidirect
14. #36475C2semidirect
15. #36448C2semidirect
18. #36431C2semidirect
19. #36380C2semidirect
20. #36199C2semidirect
21. #35971C2semidirect
22. #35883C2semidirect
23. #35868C2semidirect
24. #35786C2semidirect
25. #34808C2semidirect
26. #34337C2semidirect
28. #34262C2semidirect
29. #34197C2semidirect
30. #34129C2semidirect
31. C4⋊C4×#41C2semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#598952
#594972
#592972
#592922
#592562
#453832
#451532
#450122
#449102
#382782
#382302
#380722
#378892
#364752
#364482
#364322
#364312
#363802
#361992
#359712
#358832
#358682
#357862
#348082
#343372
#342932
#342622
#341972
#341292
C4⋊C4×#412